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Explosive higher-order Kuramoto dynamics on simplicial complexes
(American Physical Society, 2020)
The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However the existing dynamical models defined on simplicial ...
Higher-order simplicial synchronization of coupled topological signals
(Nature Research, 2021-06-07)
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order ...
Dirac synchronization is rhythmic and explosive
(2022-10-17)
Geometry, Topology and Simplicial Synchronization
(2021-05-03)
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral ...